Free-Shape Optimization of a 3-D Bracket using the Free-shape Method In this exercise, shape optimization on a solid bracket model will be performed using the Free-Shape optimization method. The objective of this optimization is to reduce the stress by changing the geometry of the bracket model.

The essential idea of free-shape optimization, and where it differs from other shape optimization techniques, is that the allowable movement of the outer boundary is automatically determined, thus relieving users of the burden of defining shape perturbations.

The optimization problem for this tutorial is stated as:

Objective: Minimize (Max Von Mises Stress)

Constraints: No Constraints

Design variables: Grids move normal to the surface.

Problem Setup You should copy this file: free_shape3D.hm

Step 1: Import the model free_shape3d.fem into HyperMesh Desktop

Step 2: Create Free-shape Design Variables (DSHAPE Cards) 1. From the Analysis page, click on optimization.

2. Select the free shape panel.

3. Click name= and enter shape.

4. Select nodes shown in the figure (select only the face nodes that are also on shells).

Free-shape design space

5. Click create.

6. Click return to go to the main menu.

Step 3: Define a static stress response named stress on props stress_faces of type vonMises with option both surfaces

Step 4: Define an Objective Reference 7. Click obj reference.

8. Enter MAX_STR in the dobjref= field.

9. Check pos reference; this gives the value 1.0.

10. Click response and select stress.

11. Click create.

12. Click return to go back to the optimization panel.

Step 5: Define the Objective Function 13. Choose the objective panel.

14. Click the left-most toggle and select minmax.

15. Click dobjrefs and select MAX_STR.

16. Click create.

17. Click return twice to go back to main menu.

Step 6: Define the SHAPE Card Only displacement and stress results are available in the _s#.h3d file by default. In order to look at stress results on top of a shape change that was applied to the model in HyperView, a SHAPE card needs to be defined.

18. From the Analysis page, select the control cards panel.

19. Select SHAPE.

20. Use the green next button to see more cards.

21. Set both TYPE and OPTION to ALL.

22. Click return twice to go back to the main menu.

Step 7: Run the optimization.

Step 8: View Shape Change results for the last (free_shape3d_s1.h3d)

Step 9: View a Contour Plot of the Stress on Top of the Shape Optimized Model

23. Go to the Contour panel and select Element Stresses [2D & 3D] as the Result type:. 24. Select von Mises as the stress type.

25. Click Apply.

The stress contour shows on top of the shape changes applied to the model.

OPTIONAL: Setup a New Free-shape Optimization Simulation with Moving Constraints. In the previous run, no constraints were applied on the movement of the DSHAPE grids. Therefore, grids are free to move and the part thickness increases as shown in the figure below.

Free-shape results without constraints

In practice, however, there will be some sort of constraints imposed upon the movement of grids due to manufacturability. For this tutorial model, thickness must be unchanged to avoid any interference with other parts.

The next step will describe how to define constraints on DSHAPE grids such that the thickness of design space will remain unchanged.

Step 10: Add Constraints on DSHAPE Grids The constraints on free-shape design grids will be created separately for curved and flat parts of the design space. The parts of the design space that are grouped as curved and those grouped as flat are illustrated in the figure below.

Design space on curved and flat part

The constraints on the curved part will be created using a local rectangular coordinate system (the other constraints on the flat part do not need a local coordinate system). Therefore, a local rectangular coordinate system (z-axis will point to normal to DSHAPE surface) needs to be created first.

26. Back in HyperMesh, click return and go to 1D page.

27. Click systems.

28. Choose the create by axis direction subpanel.

29. Click nodes and select node ID 20999 (See the following figure).

30. Click origin and select the same node (ID 20999) as nodes.

31. Click x-axis and select node ID 15989.

32. Click xy-plane and select node ID 19462.

Local coordinate system

33. Click create.

34. Click return.

35. From the Analysis page, click on optimization.

36. Select the free shape panel.

37. Select the gridcon subpanel.

The constraints on the flat part will be created first without any coordinate system.

38. Click desvar= and select shape.

39. Select constraint type as planar. 40. Select nodes shown in the following figure.

Constraints on Free Shape design space

41. Click the vector definition switch and select vectors.

42. Select N1, N2, N3 as those three nodes on plane geometry (as shown in the figure below).

Three nodes to defined the plane

43. Click add.

These nodes will move only on the specified plane above. Next, the constraints on the curved part will be created using a local coordinate system.

44. Select constraint type as vector. 45. Click nodes.

46. Select nodes shown in the following figure (select only the nodes that are on the curved part).

Constraints on free-shape design space on curved part

47. Click the direction selector and select local system.

48. Select the local coordinate system created in the previous step.

49. Click the vector definition switch and select vector. 50. Click the direction definition switch below vector, and select z-axis from the pop-up menu.

51. Click add.

52. Click return twice to get back to the main menu.

Step 11: Re-run the model 53. From the Analysis page, click OptiStruct. 54. Click save as… following the input file: field.

55. Select the directory where you would like to write the OptiStruct model file and enter the name for the model, Free_Shape3D_const.fem, in the File name: field.

56. Click Save.

Note that the name and location of the Free_Shape3D_const.fem file is displayed in the input file: field.

57. Set the memory options toggle to memory default. 58. Click the run options switch and select optimization.

59. Set the export options toggle to all. 60. Click OptiStruct.

Step 12: Post-process the New Free-shape Optimization Results. Follow the previously described steps on how to post-process the results (optimization results without constraints) using HyperView, and compare the final shape change and stress results.